Does Zenith Blade's 'you may move a friendly unit' effect count as choosing, for cards like Irelia?

Yes. Riftbound uses a negative definition of targeting and choosing: everything you decide counts as a choice unless it falls into one of a few specific exceptions, such as choices made in a private zone like your hand, being a targeting restriction for another effect, being part of a cost/condition/replacement effect, being programmatically selected with no real decision, being decided in part by other players, or using the word 'must'. Deciding which friendly unit to move with Zenith Blade doesn't fall into any of those exceptions — even if you only have one legal unit to move — so it counts as choosing for abilities like Irelia's, even though the card never says 'choose'.